Interpolation and Mapping in Fluid-Structure Interaction: Connecting the Dots
FSI often involves transferring data between two incompatible meshes—fluid and structure. To wrap-up the whole series, let’s dive into the processes of mapping and interpolation, essential for bridging the gap between these domains.
In the world of FSI, the fluid-structure interface is where the action happens. This is the boundary where the fluid and structural models interact, exchanging forces, displacements, and velocities. However, in most cases, the meshes for the fluid and structure do not align. For example, a fluid's mesh might require high resolution to capture turbulence, while a structure's mesh may prioritize different details, such as stress concentrations. This mismatch requires advanced techniques to transfer data seamlessly across the interface.
Data Transfer Process
The data transfer process in FSI involves four key components:
Data Pre-processing:
Converts nodal data to face/element data and vice versa.
Prepares the mesh data for mapping and interpolation.
Mapping:
Matches source mesh nodes (sender) to target mesh elements (receiver).
For example, mapping fluid forces to the structure's surface or structural displacements back to the fluid.
Interpolation:
Projects data from the source mesh to the target mesh.
Generates weights to ensure data is accurately transferred.
Uses methods like nearest neighbor, projection-based, or spline-based techniques.
Post-processing:
Stabilizes the interpolated data, removes non-physical values, and ensures smoothness.
Mapping Algorithms
Mapping establishes the connection between source and target meshes, ensuring data like displacements and forces are accurately passed.
Global Method:
Loops through all nodes and elements to find the closest match.
Computationally expensive for large models.
Bucket Search Algorithm:
Divides the domain into smaller "buckets" to reduce search areas.
Improves efficiency by only testing elements within the bucket of interest.
Smart Buckets: Adjusts bucket sizes dynamically for unevenly distributed meshes.
Interpolation Techniques
Interpolation transforms data from the mapped source nodes into values usable by the target nodes.
Nearest Neighbor Interpolation
Transfers data from the closest source node to the target node.
Limitations: Works best for nearly identical meshes.
Projection-Based Methods
Projects a target node onto the source mesh and interpolates data based on its relative position.
Used for high-accuracy FSI simulations.
Spline-Based Methods
Constructs a smooth surface that passes through all source points.
For example, Infinite-plate spline or Radial Basis Functions (RBFs).
Conservative vs. Non-Conservative Interpolation
Conservative: Ensures global properties like force or energy are conserved.
Non-Conservative: Focuses on maintaining local profiles, such as displacement or temperature gradients.
Conclusion
Mapping and interpolation are the true heroes of FSI simulations, ensuring seamless data transfer between incompatible meshes. By mastering these techniques, engineers can unlock the full potential of FSI to solve complex, real-world problems.